48÷2(9+3) =

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Cheesetogo

Diamond Member
Jan 26, 2005
3,817
5
81
read the article linked in my earlier post. There are plenty of sources that say that multiplicaton takes precedence over division - it's not just a "misleading guideline". According to the article, this is in fact the classical definition of mathematical order of precedence, which would make the answer 2.

I did not read the entirety of the article you posted, but I did search for division and read everything mentioned on that. From the sound of it, this does not come from definition but rather an assumption.

It seems silly to take these assumptions over the definition used in pretty much all of modern algebra.
 

James3shin

Diamond Member
Apr 5, 2004
4,426
0
76
read the article linked in my earlier post. There are plenty of sources that say that multiplicaton takes precedence over division - it's not just a "misleading guideline". According to the article, this is in fact the classical definition of mathematical order of precedence, which would make the answer 2.

In the quote you linked, the natural order did not distinguish between multiplication or division.

Mathforum said:
In summary, I would say that the rules actually fall into two
categories: the natural rules (such as precedence of exponential over
multiplicative over additive operations
, and the meaning of
parentheses), and the artificial rules (left-to-right evaluation,
equal precedence for multiplication and division, and so on). The
former were present from the beginning of the notation, and probably
existed already, though in a somewhat different form, in the geometric
and verbal modes of expression that preceded algebraic symbolism. The
latter, not having any absolute reason for their acceptance, have had
to be gradually agreed upon through usage, and continue to evolve.

It seems to me they are treating division as the multiplication of the reciprocal. Also in the wiki link provided by HAL9000, the order of operation does not have multiplication ahead of division, instead they are lumped together as "multiplication and division". Further reading of the wiki link also states that "It is helpful to treat division as multiplication by the reciprocal (multiplicative inverse) and subtraction as addition of the opposite (additive inverse)." Now, wiki is not the best source but both, your source and wiki clearly do NOT put multiplication over division and at best, they lump the two as one and the same via multiplicative inverse.

I feel the answer to this math question is unambiguously 288.
 

James3shin

Diamond Member
Apr 5, 2004
4,426
0
76
Upon further reading at the Math Forum posted by NuclearNed, I came across:

3. Some of the specific rules were not yet established in Cajori's own
time (the 1920s). He points out that there was disagreement as to
whether multiplication should have precedence over division, or
whether they should be treated equally. The general rule was that
parentheses should be used to clarify one's meaning - which is still
a very good rule.

Multiplication does NOT have precedence over division. Parentheses are our friends. But only when they are there.
 

zinfamous

No Lifer
Jul 12, 2006
111,110
30,063
146
As a test, I calculated this while I was walking on my treadmill.

the answer is still 2.
 

SunnyD

Belgian Waffler
Jan 2, 2001
32,674
146
106
www.neftastic.com
.99999999999999etc= .99999999999999etc

.9...=1

Ergo:

.9999.....9 = 1

Therefore .9999.....89 = .9999.....9 = 1

Therefore .9899.....99 = .9999.....9 = 1

Therefore .9899.....98 = .9999.....9 = 1

(Skipping ahead a few)

Therefore .9889.....99 = .9999.....9 = 1

(Skipping ahead a bunch more)

Therefore .0000.....01 = .9999.....9 = 1

Therefore 0 = 1.
 

Matthiasa

Diamond Member
May 4, 2009
5,755
23
81
Ergo:

.9999.....9 = 1

Therefore .9999.....89 = .9999.....9 = 1

Therefore .9899.....99 = .9999.....9 = 1

Therefore .9899.....98 = .9999.....9 = 1

(Skipping ahead a few)

Therefore .9889.....99 = .9999.....9 = 1

(Skipping ahead a bunch more)

Therefore .0000.....01 = .9999.....9 = 1

Therefore 0 = 1.

Just no.
All of those are finite so even the first one isn't true.
 

fatpat268

Diamond Member
Jan 14, 2006
5,853
0
71
read the article linked in my earlier post. There are plenty of sources that say that multiplicaton takes precedence over division - it's not just a "misleading guideline".

I feel like I'm being trolled here...

There is still some development in this area, as we frequently hear
from students and teachers confused by texts that either teach or
imply that implicit multiplication (2x) takes precedence over
explicit multiplication and division (2*x, 2/x)
in expressions
such as a/2b, which they would take as a/(2b), contrary to the
generally accepted rules. The idea of adding new rules like this
implies that the conventions are not yet completely stable; the
situation is not all that different from the 1600s.

Pure bullshit. The only reason why that even occurs is because of the ambiguity of the notation. Their example a/2b is only confusing when typed.

When written, it'd be
a
2b
and there would be zero confusion. As it's written, a/2b should be (a/2)*b, and it always will. Get rid of the ambiguity and just write it as a/(2b), and once again, there wouldn't be a problem.

You can't just pick and choose when the order of operations work or not.
 

mjrpes3

Golden Member
Oct 2, 2004
1,876
1
0
I went with 2. Excel says 288.

It's the shitty way it's written. Once we got past grade 3, my math teachers almost never touched the divide symbol. Since you can't type denominators, it is often assumed that anything to the right of "/" or the divide symbol is part of the denominator.

This. I see 48 / X(Y+Z) and assume (badly) X(Y+Z) is the the full denominator, because that's how I visually see the expression in my head.

If the expression was written 48/2 * (9+3), then it's clear 48/2 is a simple fraction separate from (9+3) and we'd all get the correct result.

This is why god invented latex.
 

SSSnail

Lifer
Nov 29, 2006
17,458
82
86
Not really. You made the implied * explicit without doing so for the implied ().

Plug the correct interpretation in:
48/(2*(9+3))
Except, the original equation doesn't have the extra set of (). If it had, then the answer is 2. You can't just go around adding shits in that aren't there and say "implied". It's either YES, or NO. ON or OFF. This is not a religion. It's not up for debate. It's not up to your "interpretation". Do you see an extra set of brackets in the original equation? NO!
 

fatpat268

Diamond Member
Jan 14, 2006
5,853
0
71
Not really. You made the implied * explicit without doing so for the implied ().

Plug the correct interpretation in:
48/(2*(9+3))



There is no difference between implied and explicit multiplication. It's all in your head.
 

Locut0s

Lifer
Nov 28, 2001
22,205
43
91
So the answer people is. Without additional bracket(s) it's somewhat ambiguous!
 

Caecus Veritas

Senior member
Mar 20, 2006
547
0
0
I can never fail a math class EVER again!! So MANY solutions!!!

48/2(9+3)/2(3+3)/2(1+3)= x
---------------------------
48/2*12/2*6/2*4 = 1728

OR

48/2(12)/2(6)/2(4)=
48/24/12/8=

a. 2/12/8=
b. 48/2/8=
c. 2/3/2=
d. .......
 

SSSnail

Lifer
Nov 29, 2006
17,458
82
86
so the answer people is. Without additional bracket(s) it's somewhat ambiguous!
i can do even bigger font.

There's nothing ambiguous about it. It's not there, it never existed. End of freaking story. Go back to school.
 

Locut0s

Lifer
Nov 28, 2001
22,205
43
91
i can do even bigger font.

There's nothing ambiguous about it. It's not there, it never existed. End of freaking story. Go back to school.

So what is your answer to the sources posted so far, some from math resources, and those who have math degrees, who say that in the world of mathematics (not comp sci) it can be somewhat ambiguous.
 
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